Consequently, we performed simulations to know how many Voronoi facets contribute to the 3dB-margin quasi-MLD error probability for random MIMO lattices generated by a matrix \(G\)  with random i.i.d \(\mathcal {N}(0,1)\)  components. We numerically generated 200000 random MIMO lattices \(\Lambda \)  and computed the average number of lattice points in a sphere of squared radius \(2\cdot d^2(\Lambda )\)  centered at the origin.
The results are reported in Table REF . Figure REF  also provide the distribution for \(n=14\) .
The random lattices in dimension \(n=14\)  are generated by a matrix \(G\)  with random i.i.d. \(\mathcal {N}(0,1)\)  components. We numerically generated 200000 random lattices in dimension \(n=14\)  to estimate the probability distribution.
For comparison, the number of points in such a sphere is 25201 for the dense Coxeter-Todd lattice in dimension 12 and 588481 for the dense Barnes-Wall lattice in dimension 16 [1]}. Note however that while the numbers shown in Table REF  are relatively low, the increase seems to be exponential: The number of lattice points in the sphere almost doubles when adding two dimensions.
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